Animales Sueltos' beginnings date back to 2004, when ZorroRe and Gato Gris went camping to a shelter for climbers situated between the cities of Mar del Plata and Balcarce. The following year, they took the initiative to start having an annual camp open for all the fandom. From 2005 to 2009, this encounter was held annually under the name of the UFA (Unión Furry Argentina). In 2010 the name UFACamp was removed, following a general tendency of organizing every furry event independently.

The convention usually took place during summer holidays in the northern hemisphere, and people from different parts of Argentina attended, occasionally from other countries too. The location chosen each year has been "La Serranita", in Colinas Verdes, 24 Km. away from Mar del Plata city. Attendance grew throughout the years; starting with 7 people in 2005, subsequent years attracted, 9, 11, 13, 20, 31 and 41 campers.